Let the total number of experts be N. E is the set of experts who voted for miss A. F is the set of experts who voted for miss B. Since 6 did not vote for either, n(E∪F)=N−6. n(E)=N2,n(F)=23N and n(E∩F)=10 . So, N−6=N2+23N−10 Solving the above equation gives N6=4⇒N=24
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is
A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?
m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small
cages and p large animal (n < p < m). The large animals are so large that they do not fit in small
cage. However, small animals can be put in any cage. The number of putting the animals into
There is a young boy’s birthday party in which 3
friends have attended. The mother has arranged 10
games where a prize is awarded for a winning game.
The prizes are identical. If each of the 4 children
receives at least one prize, then how many
distributions of prizes are possible?